Considering they are on the same blockchain, if "everyone" is using one or the other, there will always be miners working to process the transfer on the "not used" output ?!
No, when you send a transaction, it doesn't attempt to send to multiple "versions" of the same "address" at the same time...
think of it like before SegWit... You had "1" addresses for "normal" Bitcoin addresses And "3" addresses for "MultiSig" addresses... When you sent to a 1, there wasn't some "not used output" going to a "3" address as well that miners were trying to process.
SegWit and legacy are just slightly different formats for representing the same thing... Where to assign control of some Bitcoins...
If you say, send to legacyAddressA, then ALL miners can only see a transaction that sends to legacyAddressA. If you say send to SegWitAddressA, then ALL miners can only see a transaction that sends to SegWitAddressA.